Technical Note: Watershed strategy for oceanic mesoscale eddy splitting

Abstract. To identify oceanic mononuclear mesoscale eddies, a threshold-free splitting method was developed based on the watershed. Because oceanic eddies are similar to plateaus and basins in the map of the sea level anomaly (SLA) data, the natural divisions of the basins are the watersheds between them. The splitting algorithm is based on identifying these watersheds by finding the path of steepest descent. Compared to previous splitting methods, the proposed splitting algorithm has some advantages. First, there are no artificial parameters. Second, the algorithm is robust; the splitting strategy is independent of the algorithm and procedure and automatically guarantees that the split mononuclear eddies are simply-connected pixel sets. Third, the new method is very fast, and the time complexity is O(N), where N is the number of multinuclear eddy pixels; each pixel is scanned only once for splitting, regardless of how many extremes there are. Fourth, the algorithm is independent of parameters; the strategy can potentially be applied to any possible physical parameters (e.g., SLA, geostrophic potential vorticity, Okubo–Weiss parameter, etc.). Besides, the present strategy can also be applied to automatic identification of troughs and ridges from weather charts. Because this general method can be applied to a variety of eddy parameter fields, we denoted it the Universal Splitting Technology for Circulations (USTC) method.

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Technical Note: Watershed strategy for oceanic mesoscale eddy splitting

Ocean Science ◽

10.5194/os-11-269-2015 ◽

2015 ◽

Vol 11 (2) ◽

pp. 269-273 ◽

Cited By ~ 10

Author(s):

Q. Y. Li ◽

L. Sun

Keyword(s):

Splitting Method ◽

Mesoscale Eddy ◽

Mesoscale Eddies ◽

Technical Note ◽

Automatic Identification ◽

Physical Parameters ◽

Splitting Algorithm ◽

Sea Level Anomaly ◽

Simply Connected ◽

General Method

Abstract. To identify oceanic mononuclear mesoscale eddies, a threshold-free splitting method was developed based on the watershed. Because oceanic eddies are similar to plateaus and basins in the map of the sea level anomaly (SLA) data, the natural divisions of the basins are the watersheds between them. The splitting algorithm is based on identifying these watersheds by finding the path of steepest descent. Compared to previous splitting methods, the proposed splitting algorithm has some advantages. First, there are no artificial parameters. Second, the algorithm is robust; the splitting strategy is independent of the algorithm and procedure and automatically guarantees that the split mononuclear eddies are simply connected pixel sets. Third, the new method is very fast, and the time complexity is O(N), where N is the number of multinuclear eddy pixels; each pixel is scanned only once for splitting, regardless of how many extremes there are. Fourth, the algorithm is independent of parameters; the strategy can potentially be applied to any possible physical parameters (e.g. SLA, geostrophic potential vorticity, Okubo–Weiss parameter). Besides, the present strategy can also be applied to automatic identification of troughs and ridges from weather charts. Because this general method can be applied to a variety of eddy parameter fields, we denoted it the Universal Splitting Technology for Circulations (USTC) method.

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Oceanic Mesoscale Eddy Detection Method Based on Deep Learning

Remote Sensing ◽

10.3390/rs11161921 ◽

2019 ◽

Vol 11 (16) ◽

pp. 1921 ◽

Cited By ~ 5

Author(s):

Zijun Duo ◽

Wenke Wang ◽

Huizan Wang

Keyword(s):

Object Detection ◽

Detection Method ◽

Mesoscale Eddy ◽

Mesoscale Eddies ◽

Threshold Value ◽

Small Samples ◽

Automatic Identification ◽

Detection Model ◽

Matter Transport ◽

Feature Pyramid

Oceanic mesoscale eddies greatly influence energy and matter transport and acoustic propagation. However, the traditional detection method for oceanic mesoscale eddies relies too much on the threshold value and has significant subjectivity. The existing machine learning methods are not mature or purposeful enough, as their train set lacks authority. In view of the above problems, this paper constructs a mesoscale eddy automatic identification and positioning network—OEDNet—based on an object detection network. Firstly, 2D image processing technology is used to enhance the data of a small number of accurate eddy samples annotated by marine experts to generate the train set. Then, the object detection model with a deep residual network, and a feature pyramid network as the main structure, is designed and optimized for small samples and complex regions in the mesoscale eddies of the ocean. Experimental results show that the model achieves better recognition compared to the traditional detection method and exhibits a good generalization ability in different sea areas.

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The Identification and Prediction of Mesoscale Eddy Variation via Memory in Memory With Scheduled Sampling for Sea Level Anomaly

Frontiers in Marine Science ◽

10.3389/fmars.2021.753942 ◽

2021 ◽

Vol 8 ◽

Author(s):

Rui Nian ◽

Yu Cai ◽

Zhengguang Zhang ◽

Hui He ◽

Jingyu Wu ◽

...

Keyword(s):

Flow Field ◽

Sea Level ◽

Early Stage ◽

World Ocean ◽

Mesoscale Eddy ◽

Mesoscale Eddies ◽

Circulation System ◽

Sea Level Anomaly ◽

Dynamical Mechanism ◽

Spatio Temporal

Ocean mesoscale eddies are ubiquitous in world ocean and account for 90% oceanic kinetic energy, which dominate the upper ocean flow field. Accurately predicting the variation of ocean mesoscale eddies is the key to understand the oceanic flow field and circulation system. In this article, we propose to make an initial attempt to explore spatio-temporal predictability of mesoscale eddies, employing deep learning architecture, which primarily establishes Memory In Memory (MIM) for sea level anomaly (SLA) prediction, combined with the existing mesoscale eddy detection. Oriented to the western Pacific ocean (125°−137.5°E and 15°−27.5°N), we quantitatively investigate the historic daily SLA variability at a 0.25° spatial resolution from 2000 to 2018, derived by satellite altimetry. We develop the enhanced MIM prediction strategies, equipped with Gated Recurrent Unit (GRU) and spatial attention module, in a scheduled sampling manner, which overcomes the gradient vanishing and complements to strengthen spatio-temporal features for long-term dependencies. At the early stage, the real value SLA input guides the model training process for initialization, while the scheduled sampling intentionally feeds the newly predicted value, to resolve the distribution inconsistency of inference. It has been demonstrated in our experiment results that our proposed prediction scheme outperformed the state-of-art approaches for SLA time series, with MAPE, RMSE of the 14-day prediction duration, respectively, 5.1%, 0.023 m on average, even up to 4.6%, 0.018 m for the effective sub-regions, compared to 19.8%, 0.086 m in ConvLSTM and 8.3%, 0.040 m in original MIM, which greatly facilitated the mesoscale eddy prediction. This proposed scheme will be beneficial to understand of the underlying dynamical mechanism behind the predictability of mesoscale eddies in the future, and help the deployment of ARGO, glider, AUV and other observational platforms.

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COSMO: A Conic Operator Splitting Method for Convex Conic Problems

Journal of Optimization Theory and Applications ◽

10.1007/s10957-021-01896-x ◽

2021 ◽

Vol 190 (3) ◽

pp. 779-810

Author(s):

Michael Garstka ◽

Mark Cannon ◽

Paul Goulart

Keyword(s):

Convex Sets ◽

Operator Splitting ◽

Splitting Method ◽

Computational Cost ◽

Coefficient Matrix ◽

Benchmark Problems ◽

Portfolio Optimisation ◽

Splitting Algorithm ◽

Semidefinite Programs ◽

Operator Splitting Method

AbstractThis paper describes the conic operator splitting method (COSMO) solver, an operator splitting algorithm and associated software package for convex optimisation problems with quadratic objective function and conic constraints. At each step, the algorithm alternates between solving a quasi-definite linear system with a constant coefficient matrix and a projection onto convex sets. The low per-iteration computational cost makes the method particularly efficient for large problems, e.g. semidefinite programs that arise in portfolio optimisation, graph theory, and robust control. Moreover, the solver uses chordal decomposition techniques and a new clique merging algorithm to effectively exploit sparsity in large, structured semidefinite programs. Numerical comparisons with other state-of-the-art solvers for a variety of benchmark problems show the effectiveness of our approach. Our Julia implementation is open source, designed to be extended and customised by the user, and is integrated into the Julia optimisation ecosystem.

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The impact of the planetary β-effect on the tilting vertical structure of a mesoscale eddy

10.5194/os-2018-39 ◽

2018 ◽

Author(s):

Shengmu Yang ◽

Jiuxing Xing ◽

Shengli Chen ◽

Jiwei Tian ◽

Daoyi Chen

Keyword(s):

South China Sea ◽

South China ◽

General Circulation ◽

Vertical Structure ◽

Mesoscale Eddy ◽

Maximum Velocity ◽

Circulation Model ◽

Mesoscale Eddies ◽

China Sea ◽

The Impact

Abstract. Tilting mesoscale eddies in the South China Sea have been reported recently from observed field data. The mechanism of the dynamic process of the tilt, however, is not well understood. In this study, the influence of planetary β on the vertical structure of mesoscale eddies and its mechanism is investigated using theoretical analysis and numerical model experiments based on the MIT General Circulation Model (MITgcm). The results of the both approaches show that vertical motion due to the planetary β effect and nonlinear dynamics causes a pressure anomaly in the horizontal domain which triggers the tilt of the eddy axis. The tilting distance extends to be the radius of the eddy maximum velocity. In addition, the vertical stratification is another key factor in controlling the tilt of a mesoscale eddy. External forcings such as wind and inflow current are not considered in this study, and topography is included only in a realistic South China Sea model. Therefore, mesoscale eddies with large vertical depth should have the similar axis tilt character in open oceans under the β-effect.

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r-Harmonic and Complex Isoparametric Functions on the Lie Groups $${{\mathbb {R}}}^m \ltimes {{\mathbb {R}}}^n$$ and $${{\mathbb {R}}}^m \ltimes \mathrm {H}^{2n+1}$$

Annals of Global Analysis and Geometry ◽

10.1007/s10455-020-09736-3 ◽

2020 ◽

Vol 58 (4) ◽

pp. 477-496

Author(s):

Sigmundur Gudmundsson ◽

Marko Sobak

Keyword(s):

Heisenberg Group ◽

Lie Groups ◽

Lie Group ◽

Riemannian Manifolds ◽

Harmonic Functions ◽

Semidirect Products ◽

Simply Connected ◽

Isoparametric Functions ◽

General Method

Abstract In this paper we introduce the notion of complex isoparametric functions on Riemannian manifolds. These are then employed to devise a general method for constructing proper r-harmonic functions. We then apply this to construct the first known explicit proper r-harmonic functions on the Lie group semidirect products $${{\mathbb {R}}}^m \ltimes {{\mathbb {R}}}^n$$ R m ⋉ R n and $${{\mathbb {R}}}^m \ltimes \mathrm {H}^{2n+1}$$ R m ⋉ H 2 n + 1 , where $$\mathrm {H}^{2n+1}$$ H 2 n + 1 denotes the classical $$(2n+1)$$ ( 2 n + 1 ) -dimensional Heisenberg group. In particular, we construct such examples on all the simply connected irreducible four-dimensional Lie groups.

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Extraction of Revolving Channels of Drifters around Mesoscale Eddy Centers Based on Spatiotemporal Trajectory Clustering

Journal of Atmospheric and Oceanic Technology ◽

10.1175/jtech-d-19-0007.1 ◽

2019 ◽

Vol 36 (9) ◽

pp. 1903-1916

Author(s):

Chunyong Ma ◽

Siqing Li ◽

Yang Yang ◽

Jie Yang ◽

Ge Chen

Keyword(s):

Clustering Algorithm ◽

Spatial Clustering ◽

Mesoscale Eddy ◽

Mesoscale Eddies ◽

Trajectory Clustering ◽

Satellite Altimeter ◽

Principal Mode ◽

In Situ Data ◽

Anticyclonic Eddies

The global oceanic transports of energy, plankton, and other tracers by mesoscale eddies can be estimated by combining satellite altimetry and in situ data. However, the revolving channels of particles entrained by mesoscale eddies, which could help explain the dynamic process of eddies entraining materials, are still unknown. In this study, satellite altimeter and drifter data from 1993 to 2016 are adopted, and the normalized trajectory clustering algorithm (N-TRACLUS) is proposed to extract the revolving channels of drifters. First, the trajectories of drifters are normalized and clustered by using the density-based spatial clustering of applications with noise (DBSCAN) algorithm. Next, the revolving channels of drifters around the eddy center are extracted. The ring or arc pattern in the middle of a normalized eddy appears when drifters are uninterruptedly entrained by eddies for more than 30 days. Moreover, the revolving channels of drifters in cyclonic eddies are relatively closer to the eddy center than those in anticyclonic eddies. These revolving channels suggest the principal mode of materials’ continuous motion processes that are inside eddies.

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Mesoscale Eddy Energy Locality in an Idealized Ocean Model

Journal of Physical Oceanography ◽

10.1175/jpo-d-13-036.1 ◽

2013 ◽

Vol 43 (9) ◽

pp. 1911-1923 ◽

Cited By ~ 12

Author(s):

Ian Grooms ◽

Louis-Philippe Nadeau ◽

K. Shafer Smith

Keyword(s):

Energy Budget ◽

Mesoscale Eddy ◽

Mesoscale Eddies ◽

Spatial Filter ◽

Ocean Model ◽

Energy Budgets ◽

Subgrid Scale ◽

Common Time ◽

Local Functions ◽

The Mean

Abstract This paper investigates the energy budget of mesoscale eddies in wind-driven two-layer quasigeostrophic simulations. Intuitively, eddy energy can be generated, dissipated, and fluxed from place to place; regions where the budget balances generation and dissipation are “local” and regions that export or import large amounts of eddy energy are “nonlocal.” Many mesoscale parameterizations assume that statistics of the unresolved eddies behave as local functions of the resolved large scales, and studies that relate doubly periodic simulations to ocean patches must assume that the ocean patches have local energetics. This study derives and diagnoses the eddy energy budget in simulations of wind-driven gyres. To more closely approximate the ideas of subgrid-scale parameterization, the authors define the mean and eddies using a spatial filter rather than the more common time average. The eddy energy budget is strongly nonlocal over nearly half the domain in the simulations. In particular, in the intergyre region the eddies lose energy through interactions with the mean, and this energy loss can only be compensated by nonlocal flux of energy from elsewhere in the domain. This study also runs doubly periodic simulations corresponding to ocean patches from basin simulations. The eddy energy level of ocean patches in the basin simulations matches the level in the periodic simulations only in regions with local eddy energy budgets.

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Colder and smaller : 10 years of observations of surface salinity by SMOS, Aquarius and SMAP to study mesoscale eddies in the Southern Ocean

10.5194/egusphere-egu2020-21449 ◽

2020 ◽

Author(s):

Audrey Hasson ◽

Cori Pegliasco ◽

Jacqueline Boutin ◽

Rosemary Morrow

Keyword(s):

Soil Moisture ◽

Southern Ocean ◽

European Space Agency ◽

Mesoscale Eddy ◽

Mesoscale Eddies ◽

Sea Surface ◽

Sea Surface Salinity ◽

Global Ocean ◽

Surface Salinity ◽

Sst Anomalies

Since 2010, space missions dedicated to Sea Surface Salinity (SSS) have been providing observations with almost complete coverage of the global ocean and a resolution of about 45 km every 3 days. The European Space Agency (ESA) Soil Moisture and Ocean Salinity (SMOS) mission was the first orbiting radiometer to collect regular SSS observations from space. The Aquarius and SMAP (Soil Moisture Active-Passive) missions of the National Aeronautics and Space Administration (NASA) then reinforced the SSS observing system between mid-2011 and mid-2015 and since mid-2015, respectively.Using the most recent SSS Climate Change Initiative project dataset merging data from the 3 missions, this study investigates the SSS signal associated with mesoscale eddies in the Southern Ocean. Eddies location and characteristics are obtained from the daily v3 mesoscale eddy trajectory atlas produced by CLS. SSS anomalies along the eddies journey are computed and compared to Sea Surface Temperature (SST) anomalies (v4 Remote Sensing Systems) as well as the SubAntarctic Front (SAF) position (CTOH, LEGOS). The vertical structure of the eddies is further investigated using profiles from colocated Argo autonomous floats.&#160;This study highlights a robust signal in SSS depending on both the eddies rotation (cyclone/anticyclone) and latitudinal position with respect to the SAF. Moreover, this dependence is not found in SST. These observations reveal oceanic the interaction of eddies with the larger scale ocean water masses. SSS and SST anomalies composites indeed show different patterns either bi-poles linked with horizontal stirring of fronts, mono-poles from trapping water or vertical mixing changes, or a mix of the two.This analysis gives strong hints for the erosion of subsurface waters, such as mode waters, induced by enhanced mixing caused by the deep-reaching eddies of the southern ocean.

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Random movement of mesoscale eddies in the global ocean

10.5194/egusphere-egu2020-114 ◽

2020 ◽

Author(s):

Xiaoming Zhai ◽

Qinbiao Ni ◽

Guihua Wang ◽

David Marshall

Keyword(s):

Isotropic Turbulence ◽

Mesoscale Eddy ◽

Lateral Diffusion ◽

Mesoscale Eddies ◽

Global Ocean ◽

Altimeter Data ◽

High Latitudes ◽

Turbulence Regime ◽

Low Latitudes ◽

Baroclinic Rossby Wave

In this study we track and analyze eddy movement in the global ocean using 20 years of altimeter data and show that, in addition to the well-known westward propagation and slight polarity-based meridional deflections, mesoscale eddies also move randomly in all directions at all latitudes as a result of eddy-eddy interaction. The speed of this random eddy movement decreases with latitude and equals the baroclinic Rossby wave speed at about 25&#176; of latitude. The tracked eddies are on average isotropic at mid and high latitudes, but become noticeably more elongated in the zonal direction at low latitudes. Our analyses suggest a critical latitude of approximately 25&#176; that separates the global ocean into a low-latitude anisotropic wavelike regime and a high-latitude isotropic turbulence regime. One important consequence of random eddy movement is that it results in lateral diffusion of eddy energy. The associated eddy energy diffusivity, estimated using two different methods, is found to be a function of latitude. The zonal-mean eddy energy diffusivity varies from over 1500 m2 s-1 at low latitudes to around 500 m2 s-1 at high latitudes, but significantly larger values are found in the eddy energy hotspots at all latitudes, in excess of 5000 m2 s-1. Results from this study have important implications for recently-developed energetically-consistent mesoscale eddy parameterization schemes which require solving the eddy energy budget. &#160;

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